Bones do not move geometry
If the Jib is an object in its own (different object than the crane) you should select it, then shift select the bone (in pose mode), then press Ctrl P and choose the "bone" option. In 2.8 you will have also to check the "relative parenting" bone option as shown in the picture.



The bone parenting will transform a whole object accordingly to the bone transformations, whitout deformings, but if the crane is the same object it will be moved too.

If the crane and the jib are in  the same object you have two options:

1) select in edit mode all vertices of the jib, press P and separate the jib from the rfest of the crane, then follow the same procedure.

Or

2) select the whole object, shift select the armature, press Ctrl P and choose "with empty groups". Then select the crane, in edit mode select all vertices of the jib, select the right vertex group in the properties panel and click the weight assign button.